Counting clique trees and computing perfect elimination schemes in parallel
Information Processing Letters
Computing roots of graphs is hard
Discrete Applied Mathematics
Algorithms for Square Roots of Graphs
SIAM Journal on Discrete Mathematics
Journal of Algorithms
Fast and Simple Algorithms for Recognizing Chordal Comparability Graphs and Interval Graphs
SIAM Journal on Computing
SODA '04 Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms
Recognizing Powers of Proper Interval, Split, and Chordal Graphs
SIAM Journal on Discrete Mathematics
Closest 4-leaf power is fixed-parameter tractable
Discrete Applied Mathematics
The NLC-width and clique-width for powers of graphs of bounded tree-width
Discrete Applied Mathematics
The clique-width of tree-power and leaf-power graphs
WG'07 Proceedings of the 33rd international conference on Graph-theoretic concepts in computer science
WG'07 Proceedings of the 33rd international conference on Graph-theoretic concepts in computer science
SIAM Journal on Discrete Mathematics
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Let T be a tree on a set V of nodes. The p-th powerTp of T is the graph on V such that any two nodes u and w of V are adjacent in Tp if and only if the distance of u and w in T is at most p. Given an n-node m-edge graph G and a positive integer p, the p-th tree root problem asks for a tree T, if any, such that G=Tp. Given a graph G, the tree root problem asks for a positive integer p and a tree T, if any, such that G=Tp. Kearney and Corneil gave the best previously known algorithms for both problems. Their algorithm for the former (respectively, latter) problem runs in O(n3) (respectively, O(n4)) time. In this paper, we give O(n+m)-time algorithms for both problems